Often enough e-mails get lost. My job is to find out at what point the e-mail is being dropped. Below is a list of commands I'd run on a Windows box which will allow you to simulate an e-mail being sent from you to an external user. You may need to perform these steps on your exchange box as the firewall will only allow outgoing port 25 traffic from a specific address.

nslookup
set q=mx
clientemailaddress.co.uk - (the bit of the users e-mail address after the @ sign)
(note down the name/ip of the record returned)
(exit back to cmd prompt)
TELNET mail.clientemailaddress.co.uk 25 (record returned above)
HELO mail.example
MAIL FROM:
RCPT TO:
DATA
Subject: test (press enter)
This is a test and only a test.(press enter)
.(press full stop, and then enter)
QUIT

Happy days
Ryan Partington